BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.4, Problem 23E
To determine

Find the derivative of the given function.

Expert Solution

Answer to Problem 23E

The derivative of the given function is dydx=12x(x2+1)2(x21)4 .

Explanation of Solution

Given:

The given function is y=(x2+1x21)3 .

Calculation:

  y=(x2+1x21)3

Apply chain rule.

  df(a)dx=dfdadadx

Let f=a3,a=x2+1x21

  dydx=dda(a3)ddx(x2+1x21)

Use quotient rule.

  (fg)'=gf'fg'g2

  dydx=dda(a3)(x21)ddx(x2+1)(x2+1)ddx(x21)(x21)2

Use derivative rule.

  ddx(xn)=nxn1 .

  dydx=3a22x(x21)2x(x2+1)(x21)2dydx=3a22x[x21x21](x21)2dydx=3a24x(x21)2

Substitute the value of a=x2+1x21 .

  dydx=3(x2+1x21)24x(x21)2dydx=12x(x2+1)2(x21)4

Hence the derivativeof the given function is dydx=12x(x2+1)2(x21)4 .

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